The three given points are vertices of a triangle, I assume?
For each point, draw a line that goes through that point and which is perpendicular to the opposite side of the triangle. Those three lines meet at a point called the orthocenter.
Let's find an equation of the line through (3,-2) and which is perpendicular to the line through the other two vertices:
Slope of line through (5,6) and (9,-2) is (-2-6)/(9-5) = -2
So, one of the three lines of interest has slope 1/2 and goes through the point (3,-2). Equation of line: y + 2 = (1/2)(x - 3)
y = (1/2)x - 7/2
Follow the same procedure for (5,6) or (9,-2). Then find the intersection point of the line y = (1/2)x - 7/2 and the line you obtained. That point is the orthocenter.
